We describe the application of supervised machine-learning algorithms to identify the likely multiwavelength counterparts to submillimeter sources detected in panoramic, single-dish submillimeter surveys. As a training set, we employ a sample of 695 (S-870 mu m greater than or similar to 1 mJy) submillimeter galaxies (SMGs) with precise identifications from the ALMA follow-up of the SCUBA-2 Cosmology Legacy Survey's UKIDSS-UDS field (AS2UDS). We show that radio emission, near-/mid-infrared colors, photometric redshift, and absolute H-band magnitude are effective predictors that can distinguish SMGs from submillimeter-faint field galaxies. Our combined radio + machinelearning method is able to successfully recover similar to 85% of ALMA-identified SMGs that are detected in at least three bands from the ultraviolet to radio. We confirm the robustness of our method by dividing our training set into independent subsets and using these for training and testing, respectively, as well as applying our method to an independent sample of similar to 100 ALMA-identified SMGs from the ALMA/LABOCA ECDF-South Survey (ALESS). To further test our methodology, we stack the 870 mu m ALMA maps at the positions of those K-band galaxies that are classified as SMG counterparts by the machine learning but do not have a >4.3 sigma ALMA detection. The median peak flux density of these galaxies is S-870 mu m, = (0.61 +/- 0.03) mJy, demonstrating that our method can recover faint and/or diffuse SMGs even when they are below the detection threshold of our ALMA observations. In future, we will apply this method to samples drawn from panoramic single-dish submillimeter surveys that currently lack interferometric follow-up observations to address science questions that can only be tackled with large statistical samples of SMGs.